Neutron Physics, Physics tutorial

Introduction:

The design of all nuclear systems- isotopic generators, radiation shield, reactors  and so on-  depends basically on the manner in which nuclear radiation communicate  with matter. In this part these communications are described for neutrons only with energies up to 20MeV. The majority of radiation encountered in practical nuclear instruments lies in this energy region.

Neutron Interactions: 

 It is significant to distinguish at outsets which as neutrons are electrically neutral; they are not affected by electrons in an atom or by positive charge of nucleus. As significance, neutrons go through atomic electron cloud and interact directly with nucleus. In short, neutrons crash with nuclei, not with atoms. Neutrons may interrelate with nuclei in one or more of the following ways:

1) Elastic scattering:  In this process, the neutrons strike the nucleus, which is approximately constantly in its ground state, the neutron reappear and nucleus is left in ground state. The neutron in this section is said to have elastically quickly by nucleus. In this document of nuclear reactions, this interface is condensed by symbol (n, n).

2) Inelastic scattering:  This process is indistinguishable to elastic spreading apart from that nucleus is left in an agitated state. As energy is retained by nucleus, this is clear that it is an endothermic communication. Inelastic dispersion is indicated by symbol (n, n'). The excited nucleus decays with emission of γ-rays. In this case, while these γ-rays originate in inelastic spreading, these are termed as inelastic γ-rays.                 

3) Radioactive capture: Here the neutron is captured by nucleus, and one or more γ-rays - considered as capture γ-rays- are ejected. This is an exothermic interaction and is indicated by (n, γ). As original neutron is engrossed, this procedure is the paradigm of a class of connections recognized as absorption reactions.

4) Charged-particle reactions: Neutrons may also vanish as outcome of absorption reactions of category (n, α) and (n, p). These reactions may be either endothermic or exothermic. 

5) Neutron-producing reactions: Reactions of these type (n, 2n) and (n, 3n) occur with energetic neutrons. The reactions are obviously endothermic since in (n, 2n) reaction one neutron, and in (n, 3n) reaction two neutrons are extracted from struck nucleus. The (n, 2n) reaction is especially important in reactors containing heavy water or beryllium as 2H and 9Be have freely hurdle neutrons that have effortlessly be emitted.

6) Fission: Neutrons colliding with sure nuclei may found nucleus to crack apart, that is, undergo fission. This reaction is the principal source of nuclear energy for practical implementation.

Cross Sections:

The level to which neutrons interact by nuclei is illustrated in terms of quantities termed as cross sections. These are stated by the following kind of experiment. Assume that a beam of monoenergetic (that is, single energy) neutrons impinges on a thin target of thickness 'X' and area 'a' as described in the figure below. If there are 'n' neutrons per cm3 in the beam and 'v' is the speed of the neutrons, then quantity:

I = nv

1318_Neutron Beam Striking a Target.jpg

As nuclei are small and the target is supposed to be thin, then most of the neutrons striking the target in an experiment similar to that illustrated in the figure above ordinarily pass via the target without interacting with any of the nuclei. The numbers that do collide is found to be proportional to the beam intensity, to the atom density 'N' of the target and to the area and thickness of the target. Such observations can be summarized via the equation.

Number of collisions per second = σINaX

Here 'σ' = the proportionality constant is termed as a cross section. The factor NaX in equation above is the total number of nuclei in the target. The number of collisions per second by a single nucleus is thus just σI. This follows that 'σ' is equivalent to the number of collisions per second by one nucleus per unit intensity of the beam.

There is other technique to view the theory of cross section. As already noted, a net of Ia neutrons hit the target per second. Of such, σI interacts by any given nucleus. This might be concluded thus that:

σI/aI = σ/a

This is equivalent to the probability that a neutron in the beam will collide by this nucleus. This will be clear from the above equation that σ consists of units of area. However, it is not difficult to see that 'σ' is nothing more than the effective cross-sectional area of the nucleus, therefore the word 'cross-section.

Neutron cross sections are deduced in units of barns, here 1 barn, abbreviated b, is equivalent to 10-24cm2. One thousandth of a barn is termed as a millibarn, represented as mb.

Till now it has been supposed that the neutron beam hits the whole target. Though, in most of the experiments the beam is in reality smaller in diameter than the target. In this case, the above formulas still hold, however now α refer to the area of the beam rather than the area of the target. The statement of cross section remains similar, certainly.

Each of the methods illustrated above by which neutrons interact by nuclei is represented by a characteristic cross section. Therefore elastic scattering is illustrated by the elastic scattering cross section σS; inelastic scattering through the inelastic scattering cross section, σi; the (n, γ) reaction (that is, radiative capture) via the capture cross section, σγ; fission via the fission cross section, σf; and so on. The sum of the cross sections for all the possible interactions is termed as the total cross section and is represented by the symbol σi; that is,

σi = σS + σi + σγ + σf .....

The total cross section assesses the probability that an interaction of any kind will take place if neutron strikes a target. The sum of the cross sections of all the absorption reactions is termed as the absorption cross section and is represented by σa. Therefore:

σa = σγ + σf + σp + σz + ....

Here, σp and σz are the cross sections for the (n, p) and (n, α) reactions. As illustrated in the above equation, fission, by convection, is treated as an absorption method.

To return to equation (σINaX), this can be represented as:

Number of collisions per second (in wholly target) = INσt x aX

Here, σt has been introduced as this cross section evaluates the probability that a collision of any kind might take place, as 'X' is the total volume of the target, it  follows from above equation that the number of collisions per cm3/sec in the target that is termed as the collision density F is represented by:

F = INσt

The product of the atom density 'N' and a cross section, as in above equation, takes place often in the equations of nuclear engineering; it is presented by the special symbol Σ, and is termed as the macroscopic cross section. In specific, the product Nσt = Σt is termed as the macroscopic total cross section, NσS = ΣS is termed as the macroscopic scattering cross section, and so forth. As N and σ contain units of cm-3 and cm2, correspondingly, Σ consists of units of cm-1. In terms of the macroscopic cross section, the collision density in the above equation reduces to:

F = IΣt

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